A viscous internal wave in a stratified fluid whose buoyancy frequency varies with altitude

1975 ◽  
Vol 69 (3) ◽  
pp. 615-624 ◽  
Author(s):  
D. Gordon ◽  
U. R. Klement ◽  
T. N. Stevenson
Keyword(s):  
Internal Wave ◽  
Small Amplitude ◽  
Wave Amplitude ◽  
Stratified Fluid ◽  
Similarity Solutions ◽  
Buoyancy Frequency ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Curved Paths

A viscous incompressible stably stratified fluid with a buoyancy frequency which varies slowly with altitude is considered. A simple harmonic localized disturbance generates an internal wave in which the energy propagates along curved paths. Small amplitude similarity solutions are obtained for two-dimensional and axisymmetric waves. It is found that under certain conditions the wave amplitude can increase with height. The two-dimensional theory compares quite well with experimental measurements.

Viscous effects in a vertically propagating internal wave

1972 ◽  
Vol 56 (4) ◽  
pp. 629-639 ◽  
Author(s):  
D. Gordon ◽  
T. N. Stevenson
Keyword(s):  
Circular Cylinder ◽  
Internal Wave ◽  
Natural Frequency ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Stratified Fluid ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Vertically Propagating

A circular cylinder is positioned horizontally in an incompressible stably stratified fluid which has a constant Brunt-Väisälä frequency. A vertical two-dimensional internal wave is produced when the cylinder is oscillated at this natural frequency. A small amplitude viscous similarity solution which explains the main features of the internal wave is presented.

Estimating wave heights from pressure data at the bed

2014 ◽  
Vol 743 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Linear Theory ◽  
Wave Height ◽  
Water Wave ◽  
Small Amplitude ◽  
Wave Amplitude ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Pressure Data ◽  
Hydrostatic Approximation ◽  
Wave Heights

AbstractWe provide some estimates for the wave height of a two-dimensional travelling gravity water wave from pressure measurements at the flat bed. The approach is applicable without limitations on the wave amplitude. It improves the classical estimates available if one relies on the hydrostatic approximation or on the linear theory of waves of small amplitude.

Source-sink turbulence in a stratified fluid

1994 ◽  
Vol 261 ◽  
pp. 273-303 ◽  
Author(s):  
B. M. Boubnov ◽  
S. B. Dalziel ◽  
P. F. Linden
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Qualitative Change ◽  
Stratified Fluid ◽  
Buoyancy Frequency ◽  
Density Level ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Sources And Sinks

A new method of generating turbulence in a stratified fluid is presented. The flow is forced by a symmetric array of sources and sinks placed around the perimeter of a tank containing stratified fluid. The sources and sinks are located in a horizontal plane and the flow from the sources is directed horizontally, so that fluid is withdrawn from and re-injected at its neutral density level with some horizontal momentum. The sources and sinks are arranged so that no net impulse or angular momentum is imparted to the flow. Measurements of the mixing produced by the turbulence are made using a conductivity probe to record the vertical density profile. The flow field is measured by tracking small neutrally buoyant particles which are placed within the fluid. The tracking of the particles and analysis of the flow fields are done automatically using DigImage, a recently developed suite of particle tracking software. The characteristics of the flow are found to depend on the forcing parameter F = V/Nd, where V is the mean velocity of the flow through the source orifices, d is the diameter of the sources and sinks and N is the buoyancy frequency of the stratification. At large F three-dimensional turbulence is produced within a mixed layer centred on the level of the sources and sinks. A comparison of mixing rates measured in this and more conventional experiments is made, and it is concluded that in terms of the local turbulence parameters the entrainment rates are similar. At low F, no significant mixing occurs and the flow is approximately two-dimensional with very small vertical velocities. Under these circumstances a qualitative change in the characteristics of the flow occurs after the experiment has been running for some hours. It is observed that the scale of the motion increases until there is an accumulation of the energy at the largest scale that can be accommodated within the tank. The structure of this large-scale circulation is analysed and it is found that a form of vorticity expulsion from the interior of the circulation has occurred. These results are compared with numerical simulations of two-dimensional turbulence, and some measurements of turbulent decay are discussed.

Density Wave Measurements in a Rectangular Clarifier

1983 ◽  
Vol 18 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Mark K. Watson ◽  
R.R. Hudgins ◽  
P.L. Silveston
Keyword(s):  
Power Spectrum ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Motion ◽  
Wave Amplitude ◽  
Suspended Solids ◽  
Small Volume ◽  
Density Wave ◽  
Measure Concentration ◽  
Wave Measurements

Abstract Internal wave motion was studied in a laboratory rectangular, primary clarifier. A photo-extinction device was used as a turbidimeter to measure concentration fluctuations in a small volume within the clarifier as a function of time. The signal from this device was fed to a HP21MX minicomputer and the power spectrum plotted from data records lasting approximately 30 min. Results show large changes of wave amplitude as frequency increases. Two distinct regions occur: one with high amplitudes at frequencies below 0.03 Hz, the second with very small amplitudes appears for frequencies greater than 0.1 Hz. The former is associated with internal waves, the latter with flow-generated turbulence. Depth, velocity in the clarifier and inlet suspended solids influence wave amplitudes and the spectra. A variation with position or orientation of the probe was not detected. Contradictory results were found for the influence of flow contraction baffles on internal wave amplitude.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

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